Introduction to Projective GeometryThis lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals. |
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
Common terms and phrases
algebraic angle arbitrary line arbitrary point asserted Axiom axis base points collinear points collineation of type column complete four-point concurrent concurrent lines configuration coordinate system Corollary corresponding points cosh cross ratio defined Definition Desargues diagonal points elements elliptic geometry euclidean geometry euclidean plane Exercise field find Find the equations finite first five fixed points following theorem gauge points harmonic conjugate harmonic tetrad Hence homogeneous coordinates hyperbolic geometry ideal line infinite intersection invariant points inverse involution involutory hexad Lemma Let P1 line-conic linear locus maps matrix metric gauge conic Moreover multiplication nonsingular conic nonsingular point-conic open set pairs of corresponding parameters parametrized in terms pencil picture plane plane perspective polar projective geometry projective plane Proof Let proof of Theorem properties real points satisfied Show singular sinh Specifically tangent theorem of Pappus transformation triples unique values vanishing line vector vertex vertices X TAX zero


